Problem: Solve for $x$ : $5x^2 - 50x + 105 = 0$
Dividing both sides by $5$ gives: $ x^2 {-10}x + {21} = 0 $ The coefficient on the $x$ term is $-10$ and the constant term is $21$ , so we need to find two numbers that add up to $-10$ and multiply to $21$ The two numbers $-7$ and $-3$ satisfy both conditions: $ {-7} + {-3} = {-10} $ $ {-7} \times {-3} = {21} $ $(x {-7}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -7) (x -3) = 0$ $x - 7 = 0$ or $x - 3 = 0$ Thus, $x = 7$ and $x = 3$ are the solutions.